The following table contains the observed distribution of th

The following table contains the observed distribution of the last digit of the forecasted high temperature on a certain day for n = 160 cities.

(a) Compute expected counts for the null hypothesis that all digits 0, 1, ..., 9 are equally likely to be the last digit of the forecasted high temperature.

(b) Calculate the chi-square goodness-of-fit statistic, ², for these data. (Give the answer correct to three decimal places.)
² =  

What are the degrees of freedom, df, for this statistic?
df =  

(c) State a conclusion about the null hypothesis that all digits are equally likely to be the last digit selected.
(a. Do not reject) (b. Reject) the null hypothesis. There (a. is) (b. is not)  statistically significant evidence against the hypothesis that all digits are equally likely to be the last digit of the forecasted high temperature.

Solution

Constructing an expected value table,

Digit   O   E
0   14   16
1   24   16
2   13   16
3   26   16
4   12   16
5   16   16
6   11   16
7   14   16
8   12   16
9   18   16 [ANSWER is the third column here]

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Using

chi^2 = Sum[(O - E)^2/E]

Then

chi^2 = 15.125 [ANSWER]

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As

df = a - 1 = 5 - 1 = 4 [ANSWER]

Thus, at 0.05 significance,

chi^2(crit) = 16.9189776

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As chi^2 < chi^2(crit), then:

OPTION A: DO NOT reject the null hypothesis.
OPTION B: There IS NOT evidence against the hypothesis that all digits are equally likely to be the last digit of the forecasted high temperature. [ANSWERS]